Ra's has more resources and all his men are trained elite fighters. I would also say Ra's has much more experience. According to him, the League of Shadows have been around for centuries.
On the other hand, Joker might have prep advantage, as he had a solution for every problem in the movie (well except when he finally got captured).
But then again Ra's using the microwave emitter (? ,w/e it was called) to get the hallucinogen out was pretty clever as well. And as I mentioned before, he has better resources and connections, including scientists providing weapons for him. You don't pull this type of crap off without deep connections in high places and also a lot of money. They also function on a global level, unlike the Joker, who is really just out for some crazy fun.
But overall, I think Joker is messing with an elite group that is out of his league.
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Like everyone else here, I really, really have my doubts that the Joker possesses anything approaching the amount of resources Ra's has. That being said, however, Ghul's plan was apparently laid out for years and took a considerable amount of time to pull off; there's nothing to suggest that he has years to prepare for controlling Gotham, and then the Joker gets in his way. Let me remind you that the Joker, with far less resources and time to plan was capable of launching assaults on Gotham that crippled it arguably more severely than Ra's did- he accomplished his main goal, unlike Ra's.
While the Joker's men are no match for Ra's in direct combat, they can serve their job well as virtual dummies; the Joker can use them to lure Ra's into a trap, or something like that. And then blow them all up.
I say that unless Ra's has months of prep before he attempts to conquer Gotham- in which case he will stomp- the Joker would win.
The thing with Joker is that he was killing public figures, which is relatively easier than finding out information or killing Ra's and his men. For one thing, he wouldn't even know where they were, and secondly, unlike in TDK, he won't be able to draw/lure them out by causing chaos like he did to Batman, cause the League don't give a shit if a maniac is killing people. They would just carry on with their mission.
I would say Ra's wins, personally. H2H Joker has no chance, and to say that Joker caused more damage on Gotham is ignoring the fact that Ra's got the whole thing started when he released all the prisoners/psychotics from Arkham. So really, Joker causing destruction supports Ra's plan of destroying Gotham. In a way, he's all... part of the plan, lol.
And same as mentioned by others, Joker's plans are effective against opponents who are trying to avoid collateral damage, which is a factor that doesn't affect Ra's and the League of Shadows.
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I think Ghul is far more intelligent. It was suggested that he had control over Gotham all along, anonymously. Ghul was able to obtain world wide influence with only a select few knowing his name. In a battle of wits i think Ghul is in another league. This, however, would not come down to a battle of calculated maneuvers. The Joker is to unpredictable. I'm sure Ghul wouldn't have a problem destroying the city of Gotham just to kill the Joker but only as a last resort. Depending on his current mood the Jokers' first attack could be destroying the entire city. they are both ruthless mofo's but the Jokers' lack of morals and value's would be his greatest advantage here.
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Assassinating public figures is one thing. Assassinating them after informing every single person in Gotham about the impending assassination is ANOTHER. He killed people who were heavily protected, under guard, and were known to be facing an assassination threat. He's easily a superior assassin in comparison to Ghul, at least from what we know of him.
And besides, this is a war between the Joker and Ra's Al Ghul. Ra's isn't gonna sit back and watch the Joker destroy Gotham, and then come, beat the Joker up, and take over Gotham. It's not going to work like that.
Even if it boils down to a direct confrontation, who says the Joker won't be prepared for it and manage to find a way to beat Ra's, like he managed to beat Batman (who beat Ra's. And, this is Batman after one year of heavy crime-fighting), and unlike in the case of Batman, he has no reason to not want to kill Ra's.
You are right, though, that Ra's' tactics may work better, simply because they are more subtle and calculating than the Joker's plan. Joker may be smarter (he is; he was lying to Harvey. His plan was quite calculated and brilliant, and unlike Ra's, he actually accomplished his eventual goal), but Ra's is better suited for this type of job.
I think Joker is far more intelligent, with less resources, less time, and inferior henchmen, he managed to spread widespread fear in Gotham, and actually managed to accomplish his main goal, to show that under the right circumstances, anyone can be just like him, and he did it to who was viewed as the best of Gotham, Dent.
hahaha. He was merely using his resources. Sure, he could have used similar tactics that the Joker employed but that would have meant exposing the League of Shadows. I was just throwing that out there i wasn't trying to contribute to Ghuls resume. Personally i think the Ghul and Joker characters are very much the same. The only thing that seems to separate the two characters for me, is Justice and Chaos.
__________________ "If you tell the truth, you never have to remember anything" -Twain
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Ra's beat Wayne twice. And I guaruntee at the end if Ra's wasn't distracted by the train tracks he would have killed Batman. He already had him subdued.